基于Kronecker型替换的黑盒多项式稀疏插值

本文基于新的Kronecker型替换,给出两个由黑盒表示的稀疏多项式的新确定性插值算法.令f∈R[x1,……,xn]是一个稀疏黑盒多项式,其次数上界为D.当R是C或者是有限域时,相对于已有算法,新算法具有更好的计算复杂度或者关于D的复杂度更低.特别地,对于一般黑盒模型,D是复杂度中的主要因素,而在所有的确定性算法中,本文的第二个算法的复杂度关于D是最低的.     

广西经济增长、金融发展与城乡收入差距的实证研究

探讨了经济增长及金融发展与城乡收入差距之间互动影响,刻画了三者间的逻辑关系,并基于广西1990-2017年的统计数据,运用状态空间模型及卡尔曼滤波算法对三者间动态关系进行了实证分析.结果显示:经济增长对城乡收入差距呈现倒U型曲线形态,而金融发展则显示出具有不断缩小城乡收入差距的趋势.     

Facile Synthesis of Manganese Tellurite Nanoparticles for Magnetic Resonance Imaging-Guided Photothermal Therapy

In this study, manganese tellurite (MnTeO₃) nanoparticles are developed as theranostic agents for magnetic resonance imaging (MRI)-guided photothermal therapy of tumor. MnTeO₃ nanoparticles are synthesized via a simple one-step method. The as-synthesized MnTeO₃ nanoparticles with uniform size show good biocompatibility. In particular, MnTeO₃ nanoparticles exhibit a high photothermal conversion efficiency (η = 26.3%), which is higher than that of gold nanorods. Moreover, MnTeO₃ nanoparticles also have high MRI performance. The longitudinal relaxivity (r₁) value of MnTeO₃ nanoparticles is determined to be 8.08 ± 0.2 mm ⁻¹ s⁻¹, which is higher than that of clinically approved T₁-contrast agents Gd-DTPA (4.49 ± 0.1 mm ⁻¹ s⁻¹). The subsequent MnTeO₃ nanoparticles-mediated photothermal therapy displays a highly efficient ablation of tumor cells both in vitro and in vivo with negligible toxicity. It is demonstrated that MnTeO₃ nanoparticles can serve as promising theranostic agents with great potentials for MRI-guided photothermal therapy.     

Negative thermal expansion in NbF_3 and NbOF_2:A comparative theoretical study

Thermal expansion control is always an obstructive factor and challenging in high precision engineering field. Here,the negative thermal expansion of Nb F_3 and Nb OF_2 was predicted by first-principles calculation with density functional theory and the quasi-harmonic approximation(QHA). We studied the total charge density, thermal vibration, and lattice dynamic to investigate the thermal expansion mechanism. We found that the presence of O induced the relatively strong covalent bond in Nb OF_2, thus weakening the transverse vibration of F and O in Nb OF_2, compared with the case of Nb F_3.In this study, we proposed a way to tailor negative thermal expansion of metal fluorides by introducing the oxygen atoms.The present work not only predicts two NTE compounds, but also provides an insight on thermal expansion control by designing chemical bond type.     

Performance guarantees of forward and reverse greedy algorithms for minimizing nonsupermodular nonsubmodular functions on a matroid

This letter studies the problem of minimizing increasing set functions, equivalently, maximizing decreasing set functions, over the base matroid. This setting has received great interest, since it generalizes several applied problems including actuator and sensor placement problems in control, task allocation problems, video summarization, and many others. We study two greedy heuristics, namely, the forward and reverse greedy. We provide two novel performance guarantees for the approximate solutions obtained by them depending on both submodularity ratio and curvature.     

Regular saturated graphs and sum-free sets

In a recent paper, Gerbner, Patkós, Tuza and Vizer studied regular F-saturated graphs. One of the essential questions is given F, for which n does a regular n-vertex F-saturated graph exist. They proved that for all sufficiently large n, there is a regular $K_3$-saturated graph with n vertices. We extend this result to both $K_4$ and $K_5$ and prove some partial results for larger complete graphs. Using a variation of sum-free sets from additive combinatorics, we prove that for all $k\ge 2$, there is a regular $C_{2k+1}$-saturated with n vertices for infinitely many n. Studying the sum-free sets that give rise to $C_{2k+1}$-saturated graphs is an interesting problem on its own and we state an open problem in this direction.